Whisk the flour, sugar, baking powder, baking soda and salt in a large bowl until no leavening lumps remain.
Whisk the buttermilk, eggs, melted butter and vanilla in a second bowl until smooth.
Fold the wet mixture into the dry mixture just until streaks of flour disappear; leave the small lumps alone and rest the batter for 10 minutes.
Heat a griddle over medium-low to 350°F and wipe it with half of the oil; a drop of batter should sizzle gently without smoking.
Pour scant 1/3-cup portions onto the griddle and cook until bubbles stay open and the edges look dry, 2 to 3 minutes.
Flip once and cook until the second side is golden and the center springs back, 1 to 2 minutes; oil the griddle again as needed.